A couple of things to keep in mind here with a rod engine - the main rod has to be in the same vertical plane as the centerline of the piston, has to run parallel to the piston, also the main rod has to clear the side rods and run parallel to them too. So, if you move the drivers outward to widen the gauge, the pistons have to move outward the same amount.
To narrow the gauge, you move the drivers inward. There is only a small amount of leeway you have before you can't machine the driving boxes any narrower, then your have to shorten the cross-ties of the frame to move the frame sections closer together. Then you have an issue where the frame sets in the saddle as the saddle is designed to have the frames a certain distance apart. If the gauge change is small enough, sometime simply moving the tires inward on the centers will do that. That way the rods don't move.
Making the gauge wider requires new frame cross pieces and a new saddle.
The NdeM standard gauge conversions of the former D&RGW has always fascinated me. In the late 1950's they converted these engines to from 36" to 56 1/2" gauge. The outside dimensions across the narrow gauge frame is 56". To place the drivers outside the frames and have 56-1/2" gauge would require moving the frames closer together, by over 6" on each side. This would have required new frame cross pieces. The piston rod center could now be way too wide, or there would have about 6" of extra crankpin on the main driver to keep the piston rod lined up. The extra crank pin out there would probably be prone to braking. Making the cylinder saddle fit the narrowed frame would be a problem. I bet they made all new cylinders that were a bit narrower.
At any rate, this was a MAJOR rebuild requiring complete disassembly and re-erection of the frame. A big job. All this done to get a wimpy 60-ton 2-8-2 with a 50 year old boiler. I'm sure the NdeM had some branch line somewhere where these two engines ran where nothing else could run on. They only lasted a few years after being standard gauged before being scrapped. I can't see how that was worth the effort.
Regauging geared engines is a bit more straight forward, in that the trucks are modified to the track gauge. WSLCo Heisler #3 had it's trucks re-gauged in the 1950's to be the Tuolumne Yard switcher. When WSLCo scrapped Heisler #4 about the same time, they saved the trucks. When Roaring Camp got #3, they got #4's trucks at the same time, so conversion back to 3' was easy. I was told (by Tom Shreve) that the SG trucks for #3 were kept around for years before coming the victim of some mis-guided scrap drive.
Re-gauging a Climax has the added issue of truck mounted brake cylinders. You can only squeeze the wheels in so far. Converting a SG engine to 3' would be difficult. Shays need to have the cylinders re-lined to match the gauge, other wise you have U-joint and square shaft problems.
